Uncertainty and Deviationsfrom Uncovered Interest Rate Parity

Adilzhan Ismailovy Barbara Rossi*

Univ. Pompeu Fabra ICREA-Univ. Pompeu Fabra,Barcelona GSE, and CREI.

This Draft: July 2016

Abstract: It is well-known that uncovered interest rate parity does not hold empirically.But is it really so? We conjecture that uncovered interest rate parity is more likely to holdin low uncertainty environments, relative to high uncertainty ones, since arbitrage opportu-nity gains become more uncertain in a highly unpredictable environment, thus blurring therelationship between exchange rates and interest rate di¤erentials. In this paper, we �rstprovide a new exchange rate uncertainty index, that measures how unpredictable exchangerates are relative to their historical past. Then we use the new measure of uncertainty toprovide empirical evidence that uncovered interest rate parity does hold in �ve industrializedcountries vis-a�-vis the US dollar at times when uncertainty is not exceptionally high, andbreaks down during periods of high uncertainty.

*Corresponding author: Barbara Rossi, CREI, Universitat Pompeu Fabra, c. Ramon TriasFargas 25-27, Mercè Rodoreda bldg., 08005 Barcelona, Spain. E-mail: barbara.rossi@upf.edu

yDepartment of Economics, Univ. Pompeu Fabra, c. Ramon Trias Fargas 25-27, 08005Barcelona, Spain. E-mail: adilzhan.ismailov@upf.edu

Acknowledgments. Supported by the Spanish Ministry of Economy and Competitiveness, GrantECO2015-68136-P and FEDER, UE. Barbara Rossi thanks the ECB for hospitality during thisproject and, in particular, Aidan Meyer.

J.E.L. Codes: F31, F37, C22, C53.

Keywords: Uncertainty, exchange rates, forecasting, uncovered interest rate parity, interestrates.

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1 Introduction

A well-known empirical fact in international �nance is that uncovered interest rate parity(UIRP) does not hold. UIRP states that, in the absence of arbitrage opportunities, thereturns from investments in two countries should be equalized, once they are converted inthe same currency; the implication is that interest rate di¤erentials should predict bilateralnominal exchange rate appreciations or depreciations. UIRP is an important building blockof most international macroeconomic models, and the lack of its validity is of such importanceto deserve the term "UIRP puzzle". Another puzzling empirical fact about UIRP is that,not only the coe¢ cients do not have the theoretical values predicted by the theory, but alsothat they are unstable over time. This paper tries to o¤er an explanation to both thesepuzzles by arguing that uncertainty is one of the reason explaining the empirical invalidityof the UIRP; that the coe¢ cients in UIRP regressions are more likely to be close to thevalues predicted by UIRP at times in which uncertainty is low; and that their time variationis, at least partly, due to the fact that UIRP holds when uncertainty is low but does notwhen uncertainty is high.More in detail, this paper makes two main contributions. First, it proposes a new measure

of exchange rate uncertainty. The novelty is not in the methodology to construct the newindex, which is based on Rossi and Sekhposyan (2015); rather, its application to measureexchange rate uncertainty. To our knowledge, this is the �rst paper to propose an indexof exchange rate uncertainty. We measure uncertainty at a point in time by the likelihoodof observing the realized exchange rate forecast error at that point in time relative to thehistorical distribution of exchange rate forecast errors. Since the uncertainty measure isbased on forecast errors, it clearly depends on the model used to forecast exchange rates. Tominimize the dependence on the model chosen to produce the forecasts, we use Consensussurvey forecasts, which have the nice feature of being model-free and timely incorporating alarge amount of information. These survey forecasts have been used recently by Ozturk andSheng (2016) to measure macroeconomic uncertainty; instead, we use them to construct anindex of exchange rate uncertainty.The second contribution is to make a step towards understanding why UIRP does not

empirically �t the data. In fact, typical estimates of the slope are either negative or zeroor too large to be reconciled with the theory (Froot and Thaler, 1990); UIRP also failsto produce competitive out-of-sample forecasts relative to the random walk (Meese andRogo¤, 1983a,b; 1988; Cheung, Chinn and Pascual, 2005; Alquist and Chinn, 2008) �seeRossi (2013) for a recent survey. The possible explanations that have been put forwardin the literature include, among others: the presence of time-varying risk premia (Fama,1984; Ghoshray, Li and Morley, 2011); imprecise standard errors (Baillie and Bollerslev,2000; Rossi, 2007); small samples (Chinn and Meredith, 2004; Chinn and Quayyum, 2013;and Chen and Tsang, 2011); and rare disasters, such as currency crashes (Brunnermeieret al., 2008).1 In this paper we consider an alternative explanation for the UIRP puzzle,namely the fact that the uncovered interest rate parity relationship might not hold in highly

1Brunnermeier et al. (2009) look at currency crashes and carry trades, where traders borrow low-interest-rate currencies and lend high-interest currencies. One of their �ndings is that higher levels of the VIX andTED spread predict higher future returns on the carry trade, implying larger UIRP violations.

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uncertain environments, while it is more likely to hold when uncertainty is low. In fact,when uncertainty is high, investors might postpone their investment decisions, and thuscreate deviations from what it is expected in the absence of arbitrage opportunities.This paper is related to several recent strands in the literature. The �rst strand is the

literature on the UIRP puzzle. While it is un-controversial that the UIRP does not holdat short horizons, Chinn and Meredith (2004), Lothian and Wu (2011) and Chinn andQuayyum (2013) �nd more empirical evidence in favor of UIRP at longer horizons.2 Inparticular, Chinn and Meredith (2004) argue that the lack of empirical evidence in favorof UIRP is due to small samples, and �nd that UIRP holds at longer horizons (above oneyear) in the longer sample of data they have available. Lothian and Wu (2011) examinehistorical data from 1800 to 1999, and �nd that the UIRP regression slope is positive for thelongest sample, and the strong negative relation found in the literature is a feature of thelate 1970s and the 1980s. Finally, Chinn and Quayyum (2013) extend the analysis in Chinnand Meredith (2004) by a decade and �nd that the results in the latter are robust; however,the evidence is slightly weaker, potentially because the longer sample includes the zero-lowerbound period. In this paper, di¤erently from the contributions listed above, we focus insteadon the lack of empirical validity of the UIRP in the short run, which still remain a puzzlein the literature, and argue that uncertainty plays a potentially important role in explainingthe puzzle.The second strand is the literature on uncertainty. Several recent papers have analyzed

the e¤ects of uncertainty on the macroeconomy; for example, Bloom (2009), among oth-ers, has measured uncertainty as the volatility in �nancial markets. In this paper, we usesurvey forecasts to measure uncertainty, similarly to Ozturk and Sheng (2016), who use sur-vey forecasts to measure global and country-speci�c macroeconomic uncertainty, and Rossi,Sekhposyan and Soupre (2016), who use survey density forecasts to understand the sourcesof macroeconomic uncertainty. However, di¤erently from Ozturk and Sheng (2016) andRossi, Sekhposyan and Soupre (2016), we focus on exchange rate uncertainty and measureuncertainty using a methodology that has the advantage of allowing to study asymmetries inuncertainty. The literature on the relationship between exchange rates and uncertainty is, in-stead, more limited. Berg and Mark (2016) and Mueller, Tahbaz-Salehi and Vedolin (2016),for example, study the relationship between trading strategies in exchange rate markets anduncertainty. The former study the exposure of carry-trade currency excess returns to globalfundamental macroeconomic risk. Their measure of global macroeconomic uncertainty, de-�ned as the cross-country high-minus-low conditional skewness of the unemployment gap,is a factor priced in currency excess returns. Mueller, Tahbaz-Salehi and Vedolin (2016)instead study whether trading strategies of going short on one currency and long on othercurrencies exhibits signi�cantly larger excess returns on FOMC announcement days, and �ndthat the excess returns are higher the higher is uncertainty about monetary policy. Belke andKronen (2015) analyze the role of uncertainty in explaining exchange rate bands of inactionand their e¤ects on exports. Our paper also studies the e¤ects of uncertainty in exchangerate markets, but focuses on explaining the UIRP puzzle, as opposed to explaining largerexcess returns in cross section carry-trade strategies or �uctuations in exports.

2This �nding mirrors the empirical �nding that monetary models of exchange rates are more likely tohold at long horizons (Mark, 2005).

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This paper is organized as follows. The next section describes the data used in thisstudy and Section 3 discusses the exchange rate uncertainty index that we use. Section 4revisits the empirical evidence on UIRP in our sample, while Section 5 investigates whetherdeviations from UIRP can be explained by uncertainty. Section 6 concludes.

2 The Data

We collect monthly data spanning 1993:M11 to 2015:M1 on exchange rates, three-month Eu-ribor rates, and the uncertainty measure. We focus on industrialized countries, and consider�ve currency pairs: the Swiss franc, the Canadian dollar, the British pound, the Japaneseyen, and the Euro against the US dollar. We focus on exchange rates for industrializedcountries for which the survey expectations necessary to construct our uncertainty index areavailable. The period has been chosen based on the availability of the uncertainty index.In fact, the data on our uncertainty measure start in 1993:M11 and end in 2015:M1 for allcurrencies except the Euro (for the Euro it begins on 2011:M7) �see below for more detailson the uncertainty measure. The data on the exchange rates for the �ve currency pairsare from WM/Reuters. The exchange rates are values of the national currencies relative toone US dollar. For the interest rates we collect monthly data on three-month Euribor ratesfor the respective �ve countries and the United States. The data are from the FinancialTimes. All data have been collected via Datastream. More details (including mnemonics)are provided in Table 1.

INSERT TABLE 1 HERE

3 The Exchange Rate Uncertainty Index

Regarding uncertainty, several methodologies and strategies to construct uncertainty in-dices are available. Bloom (2009) proposes to measure macroeconomic uncertainty using thevolatility in stock prices, while Baker, Bloom and Davis (2016) propose a measure of macro-economic policy uncertainty. Since we are interested in exchange rate uncertainty, we cannotuse their measure. Jurado, Ludvigson and Ng (2015) propose to measure uncertainty as thetime-varying volatility of forecast errors in predicting exchange rates while Scotti (2016) mea-sures uncertainty as macroeconomic news announcements. The uncertainty series that weuse are similar in spirit to Jurado, Ludvigson and Ng (2015) but they are obtained using themethodology in Rossi and Sekhposyan (2015). Rossi and Sekhposyan�s (2015) uncertaintyindex is constructed by comparing the realized forecast error of the target variable with theunconditional forecast error distribution of the same variable. The intuition is that, if theobserved realization of the forecast error is in the tails of the distribution, then the realiza-tion was very di¢ cult to predict; thus, such an environment is deemed very uncertain. Oneof the advantages of the Rossi and Sekhposyan (2015) index is that it allows for asymmetry:in other words, it can separately distinguish between uncertainty due to unexpectedly high

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and low exchange rates � an important feature that is not shared by uncertainty indicesbased on the volatility of forecast errors.We construct the exchange rate uncertainty index based on forecast errors from surveys

conducted by Consensus Economics. The uncertainty index is monthly and the forecasthorizon is three months; therefore, the interest rate di¤erential is based on three-monthsinterest rates. Let the bilateral nominal exchange rate between a country and the US attime t be denoted by St and let st = ln (St). Furthermore, let the h�step-ahead forecasterror for the rate of growth of the exchange rate between time t and time t+h be denoted byet+h = (st+h � st)�Et(st+h�st); and its unconditional forecast error distribution be denotedby p (e). Rossi and Sekhposyan�s (2016) index is based on the cumulative density of forecasterrors evaluated at the realized forecast error, et+h: Ut+h =

R et+h�1 p (e) de: A large value of the

index (which takes values between zero and one) indicates a realization of the exchange ratethat is very di¤erent from the expected value. In particular, a realized value much biggerthan the expected value measures a positive �shock�, while a value of the index close tozero indicates situations where the realized value was much smaller than the expected value,identifying a negative unexpected �shock.�To convey information about the asymmetry inuncertainty, Rossi and Sekhposyan (2016) propose to construct �positive�and a �negative�uncertainty indices (relative to the average value of uncertainty) over time, as follows:

U+t+h =1

2+ max

�Ut+h �

1

2; 0

�; U�t+h =

1

2+ max

�1

2� Ut+h; 0

�: (1)

Note that U+t+h measures uncertainty associated with situations where the exchange rateturns out to be higher than expected, while U�t+h measures uncertainty associated withsituations where the exchange rate turns out to be lower than expected. Note that theuncertainty is measured such that unexpectedly low exchange rate values correspond to anunexpected depreciation of the US dollar relative to the reference currency (or an unexpectedappreciation of the reference currency).We refer to U+t+h as a measure of upside uncertainty, and to U

�t+h as a measure of downside

uncertainty. Note that, by construction, the indices have values between 0.5 and 1. We alsoconsider an overall uncertainty index, de�ned as:

U�t+h =1

2+

����Ut+h � 12���� :

Figure 1 plots the overall uncertainty indices for the countries in our sample. The timeseries �uctuations of the uncertainty indices are consistent with several events that havea¤ected these countries over time. For example, focusing on Europe, the two periods of highuncertainty during the latest �nancial crisis are clearly visible; they are related to the tworecent recessions in the Euro-area: the �rst from 2008:Q1 to 2009:Q2 and the second from2011:Q3 to 2013:Q1. In particular, the Euro debt crisis shows up as an upward trend inuncertainty in Europe since mid-2011. A similar pattern a¤ects the UK during the sameperiod. Note also the upward trend in uncertainty is visible in Canada during the recent US�nancial crisis starting in 2007. Finally, another notable event taking place in 2006 is Bankof Japan raising interest rates for the �rst time in several years, which might have causedthe drastic increase in uncertainty around mid-2006.

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INSERT FIGURE 1 HERE

4 Revisiting Uncovered Interest Rate Parity

Uncovered interest rate parity (UIRP) states that, in a world of perfect foresight and anominal bilateral exchange rate St, investors can buy 1=St units of foreign bonds usingone unit of the home currency, where St denotes the price of foreign currency in terms ofhome currency. Suppose the foreign bond pays one unit plus the foreign interest rate be-tween time t and (t+ h), i�t+h, where h is the horizon of the investment. At the end ofthe period, the foreign return can be converted back in the home currency with a value ofSt+h

��1 + i�t+h

�=St�in expectation. In the absence of transaction costs, by arbitrage this

return must be in expectation equal to the return of the home bond, (1 + it+h). Therefore,�1 + i�t+h

�Et (St+h=St) = (1 + it+h), where Et (:) denotes the expectation at time t. By tak-

ing logarithms and ignoring Jensen�s inequality, the uncovered interest rate parity equationfollows directly:

Et (st+h � st) = �+ ��it+h � i�t+h

�; (2)

where the UIRP parameters � and � have the theoretical values: � = 0 and � = 1.Overall, the empirical evidence is not favorable to UIRP �see Rossi (2013) for a recent

survey. It is well-known that the constant, �, is di¤erent from zero, and the slope, �, iseither negative or close to zero, or sometimes positive and very large in magnitude. Simi-larly, the empirical evidence is equally not supportive of the UIRP in out-of-sample forecastevaluations; in fact, it is also well-known, since the early work by Meese and Rogo¤ (1983a,b;1988), that eq. (2) does not forecast exchange rates out-of-sample better than the randomwalk. The same result was reinforced by Cheung, Chinn and Pascual (2005) and Alquist andChinn (2008). Slightly more positive �ndings have been reported by Clark and West (2006)at short-horizons; however, as Rossi (2013) pointed out, the reason for the positive �ndingsin Clark and West (2006) are mainly due to the use of new and di¤erent test of predictiveability.We start by con�rming the existing �ndings in the literature, namely that UIRP does not

hold in the data. Panel A in Table 2 estimates regression (2) in our sample, and shows that,for several countries, � is very small, and in the case of Switzerland, Canada and Japan, it isnegative and statistically signi�cantly di¤erent from one. Only for Europe and the UK theslope is positive and statistically indistinguishable from its theoretical value under the UIRP.The constant instead is small and insigni�cantly di¤erent from zero for most countries.3

Our results are similar to those in the literature, except that our estimates are slightlysmaller than those reported in the earlier literature. For instance, Chinn and Quayyum(2013) use quarterly data spanning the period of 1975:Q1-2011:Q4 for the same set of cur-rency pairs, and they �nd slope estimates ranging from -1.85 to -2.25 with the exception ofthe Canadian dollar, whose slope is -0.17. However, a detailed analysis reveals that the large

3The con�dence intervals are constructed based on a Newey and West (1987) HAC estimator for thecovariance matrix, using a truncation lag equal to two.

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negative values are driven by sample selection. Firstly, the rolling-window estimates whichwe report later in the paper show that the slope coe¢ cients have been increasing over time:our sample is shorter than, e.g., Chinn and Quayyum (2013), and in particular it omits theSeventies and the Eighties; the latter are decades with large deviations from UIRP accordingto Lothian and Wu (2011).4 Secondly, if we consider the sample up to 2011:M10, that is,omitting the last 4 years to better match the sample used in Chinn and Quayyum (2013),the estimates become negative for four countries out of �ve and the negative coe¢ cients arelarger in magnitude. The results are reported in Table 2, Panel B.

INSERT TABLE 2 HERE

A comparison of the results in the two panels in Table 2 also points out another importantempirical feature of UIRP: the well-known fact that the UIRP parameters are unstable overtime. In fact, note how, for example, the slope coe¢ cient for the Euro data turns frompositive to negative depending on the sample, and how its magnitude varies in Japanese data.Rossi (2006) investigates the instability in the parameters in exchange rate monetary models(that is, models that explain exchange rate �uctuations using output, money and interestrate di¤erentials) and �nds ample evidence of instabilities based on conventional tests ofparameter instability. Furthermore, she argues that the empirical rejections of the monetaryexchange rate model can be due to parameter instabilities; in fact, by using alternative andmore powerful tests that evaluate Granger-causality robust to instabilities, she �nds thatmonetary models�predictors helped forecasting exchange rates at some point in time.We investigate the stability of the UIRP parameters over time by plotting their estimates

in rolling windows over ten years of data in the top panel in Figures 2(a-e). The �gurescon�rm the presence of instabilities throughout the sample that we consider. For Canada, thevalue of the constant is small throughout the sample, but the slope value changes signi�cantlyfrom negative to positive. The slope changes drastically for Europe as well, ranging fromvalues close to zero at the beginning of the sample to almost four towards the end of thesample. In the case of Japan, the coe¢ cient is close to zero for almost all the sample exceptthe beginning and the end. Switzerland and the UK are two other countries where the slopechanges drastically from negative values to large and positive values. For the latter country,the constant also is very unstable, taking both positive and negative values depending onthe sample period.

INSERT FIGURE 2 HERE

We investigate more formally whether instabilities a¤ect UIRP in Table 3(a-c). Weconsider the following regression:

Et (st+h � st) = �t + �t�it+h � i�t+h

�; (3)

4Our sample is shorter since it is determined by the availability of the uncertainty index.

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where the constant, or the slope parameter, or potentially both, might be time-varying.Absence of time variation manifests itself in constant parameters, that is: �t = � and/or�t = �. We test parameter stability using a battery of tests, including Andrews� (1993)Quandt Likelihood Ratio test (QLR), Andrews and Ploberger�s (1993) Exponential-Wald(Exp-W) and Mean-Wald (Mean-W) tests, as well as Nyblom�s (1989) test. The tests dif-fer depending on the type of instability they allow for; in particular, Andrews (1993) andAndrews and Ploberger (1993) allow for one-time structural changes while Nyblom (1989)considers smoother and more frequent changes.Table 3(a) reports results for testing the joint instability in both the constant and the

slope parameters. It is clear that the stability is overwhelmingly rejected, with p-values thatare zero in all cases. We then investigate whether the instability is more pronounced in theconstant or in the slope. Table 3(b) reports tests of stability on the constant. The tableshows that the constant is unstable for most countries except the UK. A time-varying �may be evidence of a time-varying risk premium. Table 3(c) reports tests of stability on theslope; the table shows that the slope is unstable for all countries, including the UK.

INSERT TABLE 3 HERE

Since the parameters are time-varying, the UIRP tests presented in Table 2 are invalid,as they assume stability in the parameters. Therefore, we complement the analysis withtests that are robust to parameter instabilities. In particular, we implement the Exp-W*,Mean-W*, Nyblom* and QLR* tests proposed by Rossi (2005), which are valid to test theUIRP conditions that �t = 0 and �t = 1 even in the presence of time-variation in theparameters.5 Tables 4(a-c) show that the results in Table 2 are robust. In particular, Table4(a) shows that the both parameters are signi�cantly di¤erent from the values predicted bythe UIRP; Tables 4(b-c) report results for the constant and the slope separately, and showthat the rejections are mostly due to the fact that the slope is di¤erent from unity, especiallyfor Canada, the UK and Japan.6

INSERT TABLE 4 HERE

The analysis in this section shows that UIRP does not hold in the data, and that thecoe¢ cients estimated in UIRP regressions are very unstable over time. However, the analysisdoes not shed light on why there are deviations from UIRP. The next section will tackle thisimportant question.

5The di¤erence among the Exp-W*, Mean-W*, QLR* and Nyblom* tests is, again, that they focus ondi¤erent types of instabilities. In particular, the �rst three focus on the case of a one-time structural changewhile Nyblom* allows smoother and more frequent changes.

6Note that, in Table 4(b), the Exp-W* test does not reject for some countries while the Mean-W*,Nyblom* and QLR* tests reject. The reason why the tests disagree is because they consider di¤erent typesof instabilities: the Nyblom* test, for example, has more power when parameters are smoothly time-varying.

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5 Can Uncertainty Explain Deviations from Uncov-ered Interest Rate Parity?

The previous section has con�rmed the existence of two important puzzles in the empiricalliterature in international �nance: UIRP coe¢ cients are both di¤erent from their theoreticalvalues and unstable over time. This paper tries to o¤er an explanation to both these puzzlesby arguing that uncertainty is one of the reason explaining the empirical invalidity of theUIRP; that the coe¢ cients in UIRP regressions are more likely to be close to the valuespredicted by UIRP in times when uncertainty is low; and that their time variation is, atleast partly, due to the fact that UIRP holds when uncertainty is low but does not whenuncertainty is high.We start our analysis by depicting our uncertainty index for each country together with

the rolling estimates of the UIRP parameters. The bottom panels in Figure 2-4 show theuncertainty index for each country. We consider the three measures of uncertainty discussedin the previous section: the bottom panels in Figures 2(a-e) plot the overall uncertainty index,U�t+h, while those in Figures 3(a-e) and 4(a-e) depict upside and downside uncertainty, U

+t+h

and U�t+h, respectively. Figure 1 shows that there is correlation between uncertainty andUIRP coe¢ cients for most countries: when uncertainty is substantially high, there are moredeviations from UIRP, both in terms of deviations of � from zero as well as deviations of� from unity. For example, the case of Switzerland (depicted in Figure 2d) is emblematic:the negative values of the slope and the constant are clearly visible at the beginning of thesample, and that is also when the uncertainty is the highest. Similarly, in the case of UK andCanada (depicted in Figures 2e and 2a, respectively), the slope is closest to unity around2005-2008, which is exactly when uncertainty is the lowest, and very di¤erent from unityboth at the beginning (when the slope is negative) and towards the end of the sample (whenthe slope is positive and large), when uncertainty is the highest. For Europe, depicted inFigure 2(b), uncertainty is high for most of the sample we consider. Finally, in the caseof Japan (depicted in Figure 2c) too, both the slope and the intercept are negative at thebeginning of the sample, when the uncertainty is often at high levels.To investigate more formally whether uncertainty can explain the UIRP puzzle, we esti-

mate the following regression:

Et (st+h � st) = �1 � (1� dt)+�1 � (1� dt) ��it+h � i�t+h

�+�2 �dt+�2 �dt �

�it+h � i�t+h

�; (4)

where dt is a dummy variable which equals one if the uncertainty is exceptionally high. Sincethe uncertainty indices are quite volatile, we smooth them out using the same rolling windowthat we used to estimate the parameters in the UIRP regression, equal to ten years of data.Time periods of high uncertainty are identi�ed by situations in which uncertainty is in theupper quartile of its distribution, i.e. we identify high uncertainty periods with sub-sampleswith the 25% highest values of uncertainty.

INSERT TABLE 5 HERE

Table 5 reports the estimates of eq. (4) when uncertainty is measured by the overalluncertainty index. The table shows that the empirical evidence in favor of UIRP is weakest

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in periods where uncertainty is exceptionally high, and substantially stronger in periodswhere uncertainty is around normal values. More in detail, we note that, in the case ofSwitzerland, both values of �2 and �2 are negative and large in absolute value; since �2 and�2 are the constant and slope of the UIRP in periods of high uncertainty, the regression resultscon�rm the existence of large deviations from UIRP when uncertainty is exceptionally high.However, in periods of low uncertainty, both �1 and �1 are closer to their theoretical values,and insigni�cantly di¤erent from them. Japan is another case where the slope switches fromnegative values (and signi�cantly di¤erent from unity) during periods of high uncertainty,to positive values close to unity (and statistically insigni�cantly di¤erent from unity). InCanada and the UK, again, the slope is negative and close to zero for the former and largeand positive for the latter in periods of high uncertainty, while it becomes positive and closerto unity in periods of low uncertainty; the constant also gets closer to its theoretical valueof zero in periods of low uncertainty. In the case of Europe, the uncertainty state also drivesthe slope coe¢ cient closer to its theoretical value; in all cases, the point estimates are moreprecisely estimated in periods of low uncertainty.Table 6 and Figures 3-4 investigate whether the type of uncertainty matters, namely

whether it is upside or downside uncertainty that is most important in resolving the UIRPpuzzle. As Table 6 shows, except for countries such as Switzerland and Europe, for whichthe downside uncertainty seems the most important one that a¤ects the slope parameters,the type of uncertainty does not matter much. Periods of downside uncertainty are typicallyassociated with a more positive slope coe¢ cient than periods of upside uncertainty in highuncertainty periods, although in both cases the slope coe¢ cients gets closer to its theoreticalvalue under the UIRP during low uncertainty times.

INSERT TABLE 6 AND FIGURES 3-4 HERE

Finally, we investigate whether uncertainty can help explaining UIRP deviations directlyby estimating the following regression:

Et (st+h � st) = �+ ��it+h � i�t+h

�+ U�t+h; (5)

where U�t+h is the measure of uncertainty, and testing whether is signi�cantly di¤erentfrom zero using the tests robust to instabilities. The results are reported in Table 7. Indeedthe table shows that uncertainty does signi�cantly help in explaining deviations from UIRPfor all countries.

INSERT TABLE 7 HERE

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6 Conclusions

This paper has investigated whether uncertainty can explain the short-run deviations fromUIRP that we empirically observe in the data. We have found that deviations from UIRPare stronger in periods of high uncertainty, while UIRP tends to hold in periods of lowuncertainty. While it is well-known that deviations from UIRP are large and time-varying,this is the �rst paper that provides an economic rationale for both the UIRP puzzle andthe presence of time variation in UIRP coe¢ cient estimates by linking UIRP deviations touncertainty.Additional analyses that could be carried out in the future include analyzing whether

other uncertainty indices may also explain UIRP deviations, e.g. the macroeconomic un-certainty indices available in the literature. However, given the well-known exchange ratedisconnect puzzle, we do not expect that to be the case. Also, one might investigate whethersimilar results hold at long horizons; however, the UIRP puzzle is really a puzzle at shorthorizons, which is what we focused on in this paper.

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Mark, N.C. (2001), International Macroeconomics and Finance: Theory and EconometricMethods, Malden, MA: Blackwell Publishers.Meese, R.A. and K.S. Rogo¤(1983a), �Empirical Exchange Rate Models of the Seventies:

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13

TablesTable 1. Data Description

Currency Period Code Full Name

Exchange rates:Swiss franc 1994M1:2015M1 SWISSF$ SWISS FRANC TO US $ (WMR) - EXCH. RATECanadian dollar 1994M1:2015M1 CNDOLL$ CANADIAN $ TO US $ (WMR) - EXCH. RATEBritish pound 1993M11:2015M1 UKDOLLR UK £ TO US $ (WMR) - EXCH. RATEJapanese yen 1993M11:2015M1 JPXRUSD JP JAPANESE YEN TO US $ - EXCH. RATEEuro 1993M11:2015M1 EUDOLLR EURO TO US $ (WMR&DS) - EXCH. RATE

Interest rates:Switzerland 1993M11:2015M1 ECSWF3M SWISS FRANC 3M DEPOSIT (FT/TR)Canada 1993M11:2015M1 ECCAD3M CANADIAN DOLLAR 3M DEPOSIT (FT/TR)United Kingdom 1993M11:2015M1 ECUKP3M UK STERLING 3M DEPOSIT (FT/TR)Japan 1993M11:2015M1 ECJAP3M JAPANESE YEN 3M DEPOSIT (FT/TR)Europe 1999M2:2015M1 ECEUR3M EURO 3M DEPOSIT (FT/TR)United States 1993M11:2015M1 ECUSD3M US DOLLAR 3M DEPOSIT (FT/TR)

Note to Table 1. The table reports mnemonics and descriptions for our data. All interestrates are "middle rates".

Table 2. Traditional UIRP RegressionsPanel A. Full Sample Panel B. Sub-sample ending in 2011

Country: � � � �Switzerland -0.01 -0.59 -0.023 -0.817

(-0.028;-0.002) (-1.09;-0.100) (-0.039;-0.007) (-1.382;-0.252)

Europe -0.007 0.391 -0.004 -0.351(-0.016;0.002) (-0.576;1.358) (-0.016;0.007) (-1.178;0.476)

Canada -0.001 -0.196 -0.003 -0.383(-0.007;0.004) (-0.706;0.312) (-0.010;0.003) (-0.906;0.140)

UK -0.004 0.378 -0.005 0.410(-0.012;0.004) (-0.513;1.271) (-0.014;0.004) (-0.502;1.324)

Japan -0.002 -0.118 -0.023 -0.585(-0.015;0.011) (-0.533;0.296) (-0.036;-0.010) (-0.988;-0.181)

Note to the table. The table reports estimates of UIRP regressions in the full sample aswell as a sub-sample ending in 2011.

14

Table 3(a). Instability Tests: Joint Test on � and �Country: QLR Exp-W NyblomSwitzerland Test statistic 39.08 15.11 3.55

P-value 0 0 0

Europe Test statistic 35.69 13.98 3.27P-value 0 0 0

Canada Test statistic 24.54 9.44 2.44P-value 0 0 0

UK Test statistic 50.09 19.9 1.98P-value 0 0 0

Japan Test statistic 44.52 18.1 4.50P-value 0 0 0

Note to the table. The table reports joint tests of parameter instabilities on the twoUIRP regression coe¢ cients.

Table 3(b). Instability Tests: Test on the Constant (�)Country: QLR Exp-W NyblomSwitzerland Test statistic 23.73 7.377 0.671

P-value 0 0 0.151

Europe Test statistic 34.06 13.52 1.978P-value 0 0 0

Canada Test statistic 16.40 4.763 0.862P-value 0 0 0.076

UK Test statistic 3.150 0.544 0.171P-value 0.809 0.828 0.847

Japan Test statistic 51.40 21.00 1.577P-value 0 0 0

Note to the table. The table reports tests of parameter instabilities on the constantcoe¢ cient in the UIRP regressions.

15

Table 3(c). Instability Tests: Test on the Slope (�)Country: QLR Exp-W NyblomSwitzerland Test statistic 26.81 8.74 1.746

P-value 0 0 0

Europe Test statistic 45.34 18.88 3.459P-value 0 0 0

Canada Test statistic 27.28 10.68 2.416P-value 0 0 0

UK Test statistic 26.44 8.54 1.06P-value 0 0 0.036

Japan Test statistic 26.66 8.92 1.176P-value 0 0 0.023

Note to the table. The table reports tests of parameter instabilities on the slope coe¢ cientin the UIRP regressions.

16

Table 4(a). Granger-causality Tests: Joint Test on � and �Country: Exp-W* Mean-W* Nyblom* QLR*Switzerland Test statistic 68.91 121.76 31.93 146.45

P-value 0 0 0 0

Europe Test statistic 23.09 26.052 6.023 54.09P-value 0 0 0 0

Canada Test statistic 57.23 89.393 16.28 120.36P-value 0 0 0 0

UK Test statistic 44.90 48.059 8.28 98.60P-value 0 0 0 0

Japan Test statistic 77.34 129.908 31.9604 163.7371P-value 0 0 0 0

Note to the table. The table reports tests of UIRP robust to parameter instabilities. Thetests are performed jointly on both the constant and the slope in the UIRP regressions.

Table 4(b). Granger-causality Tests: Test on the Constant (�)Country: Exp-W* Mean-W* Nyblom* QLR*Switzerland Test statistic 11.19 16.55 3.52 29.48

P-value 0 0 0.021 0

Europe Test statistic 11.32 13.16 3.02 29.36P-value 0 0 0.034 0

Canada Test statistic 3.948 4.095 0.677 14.143P-value 0.123 0.404 0.550 0.051

UK Test statistic 1.117 1.810 0.938 4.437P-value 0.822 0.847 0.404 0.820

Japan Test statistic 17.31 6.837 1.749 43.652P-value 0 0.121 0.153 0

Note to the table. The table reports tests of UIRP robust to parameter instabilities. Thetests are performed on the constant coe¢ cient in the UIRP regressions.

17

Table 4(c). Granger-causality Tests: Test on the Slope (�)Country: Exp-W* Mean-W* Nyblom* QLR*Switzerland Test statistic 9.363 26.81 8.74 1.746

P-value 0.002 0 0 0

Europe Test statistic 1.081 45.34 18.88 3.459P-value 0.298 0 0 0

Canada Test statistic 0.946 27.28 10.68 2.416P-value 0.330 0 0 0

UK Test statistic 1.216 26.44 8.54 1.0642P-value 0.270 0 0 0.036

Japan Test statistic 0.559 26.66 8.926 1.176P-value 0.454 0 0 0.023

Note to the table. The table reports tests of UIRP robust to parameter instabilities. Thetests are performed on the slope coe¢ cient in the UIRP regressions.

18

Table 5: UIRP and Overall UncertaintyLow Uncertainty High Uncertainty

Country �1 �1 �2 �2

Switzerland 0.001 0.469 -0.034 -9.389(-0.017;0.019) (-0.274;1.213) (-0.074;0.006) (-19.342;0.564)

Europe -0.001 1.918 -0.012 3.445(-0.015;0.013) (0.188;3.649) (-0.081;0.056) (-3.518;10.407)

Canada -0.005 1.632 -0.009 -0.114(-0.015;0.005) (0.525;2.738) (-0.041;0.024) (-4.606;4.379)

UK -0.007 0.332 -0.033 6.951(-0.017;0.003) (-0.485;1.150) (-0.067;0.000) (4.754;9.147)

Japan 0.009 0.739 -0.002 -0.331(-0.007;0.025) (0.089;1.390) (-0.030;0.026) (-1.186;0.523)

Note to the table. The table reports parameter estimates in eq. (4), where the measureof uncertainty is overall uncertainty.

19

Table 6: UIRP and Upside/Downside Uncertainty

Low Uncertainty High UncertaintyCountry �1 �1 �2 �2

Switzerland Upside Unc. 0.000 0.926 -0.005 -0.149(-0.018;0.017) (-0.011;1.863) (-0.046;0.037) (-1.599;1.301)

Downside Unc. 0.000 0.419 -0.034 -9.340(-0.018;0.018) (-0.324;1.162) (-0.083;0.014) (-20.664;1.983)

Europe Upside Unc. -0.007 1.946 0.016 1.500(-0.021;0.007) (0.349;3.543) (-0.007;0.039) (-1.062;4.061)

Downside Unc. -0.004 3.059 -0.029 -0.380(-0.021;0.013) (0.375;5.742) (-0.046;-0.013) (�1.498;0.738)

Canada Upside Unc. -0.007 1.347 -0.001 1.697(-0.019;0.005) (-0.023;2.717) (-0.016;0.013) (0.450;2.945)

Downside Unc. -0.004 1.741 -0.010 0.751(-0.017;0.009) (0.553;2.928) (-0.034;0.015) (-2.929;4.430)

UK Upside Unc. -0.010 0.312 -0.007 3.533(-0.019;-0.001) (-0.557;1.181) (-0.047;0.033) (0.288;6.778)

Downside Unc. -0.011 1.356 -0.011 2.782(-0.025;0.002) (-0.051;2.762) (-0.050;0.029) (-4.765;10.330)

Japan Upside Unc. 0.009 0.739 -0.002 -0.331(-0.007;0.025) (0.089;1.390) (-0.030;0.026) (-1.186;0.523)

Downside Unc. 0.015 0.271 -0.008 1.153(-0.002;0.033) (-0.249;0.791) (-0.029;0.012) (0.306;2.000)

Note to the table. The table reports parameter estimates in eq. (4), where the measureof uncertainty is either upside or downside uncertainty.

20

Table 7: Does Uncertainty Granger-cause Exchange Rates?Country: Exp-W* Mean-W* Nyblom* QLR*Switzerland Test statistic 68.91 121.7 31.93 146.4

P-value 0 0 0 0

Europe Test statistic 23.09 26.05 6.02 54.09P-value 0 0 0 0

Canada Test statistic 57.23 89.39 16.28 120.3P-value 0 0 0 0

UK Test statistic 44.90 48.05 8.28 98.60P-value 0 0 0 0

Japan Test statistic 77.34 129.9 31.96 163.7P-value 0 0 0 0

Note to the table. The table reports tests robust to parameter instabilities of whetheruncertainty is a signi�cant predictor in UIRP regressions.

21

Figures

Figure 1. Uncertainty Indices

Time2004 2005 2006 2007 2008 2009 2010 2011 2012

Unc

erta

inty

0.5

0.55

0.6

0.65

0.7

0.75

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1Europe

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Unc

erta

inty

0.5

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1Canada

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Unc

erta

inty

0.5

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1Japan

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Unc

erta

inty

0.5

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0.95

1UK

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Unc

erta

inty

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1Switzerland

Notes to the �gure. The �gure plots the overall uncertainty index for the countries inour sample.

22

Figure 2(a)

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

t

­0.015

­0.01

­0.005

0Canada

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Unc

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1

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

t

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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1

Figure 2(b)

Time2004 2005 2006 2007 2008 2009 2010 2011 2012

t

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0

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Time2004 2005 2006 2007 2008 2009 2010 2011 2012

Unc

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Time2004 2005 2006 2007 2008 2009 2010 2011 2012

t

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4

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Time2004 2005 2006 2007 2008 2009 2010 2011 2012

Unc

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1

Figure 2(c)

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

t

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0

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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23

Figure 2(d)

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

t

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0Switzerland

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

t

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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1

Figure 2(e)

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

t

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0

0.005

0.01UK

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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1

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

t

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3UK

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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24

Figure 3(a)

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

t

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0Canada

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Ups

ide­

Unc

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Figure 3(b)

Time2004 2005 2006 2007 2008 2009 2010 2011 2012

t

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0

0.01Europe

Time2004 2005 2006 2007 2008 2009 2010 2011 2012

Ups

ide­

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Time2004 2005 2006 2007 2008 2009 2010 2011 2012

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Time2004 2005 2006 2007 2008 2009 2010 2011 2012

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Figure 3(c)

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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25

Figure 3(d)

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

t

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0Switzerland

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Figure 3(e)

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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26

Figure 4(a)

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Figure 4(b)

Time2004 2005 2006 2007 2008 2009 2010 2011 2012

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Time2004 2005 2006 2007 2008 2009 2010 2011 2012

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Figure 4(c)

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Figure 4(d)

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Figure 4(e)

Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Time1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

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Notes to Figure 2-4. The top panels in the �gure plot the UIRP coe¢ cients estimated inrolling windows (the constant is depicted on the left and the slope on the right). The bottompanels in the �gures plot the corresponding uncertainty index, either overall uncertainty(Figure 2), upside uncertainty (Figure 3) or downside uncertainty (Figure 4).

28